Coupled heat equation in thermoelasticity with temperature dependent moduli

References

• B. A. Boley, “Survey of recent developments in the fields of heat conduction in solids and thermo-elasticity,” Nucl. Eng. Des., vol. 18, no. 3, pp. 377–399, 1972. doi: 10.1016/0029-5493(72)90109-4. DOI: 10.1016/0029-5493(72)90109-4.
   Web of Science ®Google Scholar
• D. H. Allen, “Thermomechanical coupling in inelastic solids,” Appl. Mech. Rev., vol. 44, no. 8, pp. 361–373, 1991. DOI: 10.1115/1.3119509.
   Google Scholar
• R. F. Barron and B. R. Barron, Design for Thermal Stresses. Hoboken, NJ: Wiley, 2011. DOI: 10.1002/9781118093184.
   Google Scholar
• S. Prabhakar, M. P. Païdoussis, and S. Vengallatore, “Analysis of frequency shifts due to thermoelastic coupling in flexural-mode micromechanical and nanomechanical resonators,” J. Sound Vib., vol. 323, no. 1-2, pp. 385–396, 2009. DOI: 10.1016/j.jsv.2008.12.010.
   Web of Science ®Google Scholar
• O. Brand, I. Dufour, S. M. Heinrich, and F. Josse, Eds. Resonant MEMS. Advanced Micro and Nanosystems. Weinheim, Germany: Wiley-VCH, 2015.
   Google Scholar
• C. Li, S. Gao, S. Niu, and H. Liu, “Study of intrinsic dissipation due to thermoelastic coupling in gyroscope resonators,” Sensors, vol. 16, no. 9, pp. 1445, 2016. DOI: 10.3390/s16091445.
   Web of Science ®Google Scholar
• K. Kokini, “Thermal shock of a cracked strip: effect of temperature-dependent material properties,” Eng. Fract. Mech., vol. 25, no. 2, pp. 167–176, 1986. DOI: 10.1016/0013-7944(86)90216-X.
   Web of Science ®Google Scholar
• C. Atkinson and R. V. Craster, “Fracture in fully coupled dynamic thermoelasticity,” J. Mech. Phys. Solids, vol. 40, no. 7, pp. 1415–1432, 1992. DOI: 10.1016/0022-5096(92)90026-X.
   Web of Science ®Google Scholar
• A. Zamani and M. R. Eslami, “Implementation of the extended finite element method for dynamic thermoelastic fracture initiation,” Int. J. Solids Struct., vol. 47, no. 10, pp. 1392–1404, 2010. doi: 10.1016/j.ijsolstr.2010.01.024. DOI: 10.1016/j.ijsolstr.2010.01.024.
   Web of Science ®Google Scholar
• Y. Shindo, “Thermal shock of cracked composite materials with temperature dependent properties,” in Thermal Shock and Thermal Fatigue Behavior of Advanced Ceramics, vol. 241, G. A. Schneider and G. Petzow, Eds, NATO ASI Series (Series E: Applied Sciences). Dordrecht: Springer, 1993; pp 181–192. DOI: 10.1007/978-94-015-8200-1_15.
   Google Scholar
• A. V. Ekhlakov, O. M. Khay, C. Zhang, J. Sladek, and V. Sladek, “A BDEM for transient thermoelastic crack problems in functionally graded materials under thermal shock,” Comput. Mater. Sci., vol. 57, no. Supplement C, pp. 30–37, 2012. DOI: 10.1016/j.commatsci.2011.06.019.
   Google Scholar
• X. Zhang, L. Zhang, and Z. Chu, “Thermomechanical coupling of non-Fourier heat conduction with the C-V model: thermal propagation in coating systems,” J. Therm. Stress., vol. 38, no. 10, pp. 1104–1117, 2015. DOI: 10.1080/01495739.2015.1073500.
   Web of Science ®Google Scholar
• Y. Wang, D. Liu, Q. Wang, and C. Shu, “Thermoelastic response of thin plate with variable material properties under transient thermal shock,” Int. J. Mech. Sci., vol. 104, no. Supplement C, pp. 200–206, 2015. DOI: 10.1016/j.ijmecsci.2015.10.013.
   Google Scholar
• Y. Z. Wang, D. Liu, Q. Wang, and J. Z. Zhou, “Thermoelastic behavior of elastic media with temperature-dependent properties under transient thermal shock,” J. Therm. Stress., vol. 39, no. 4, pp. 460–473, 2016. DOI: 10.1080/01495739.2016.1158603.
   Web of Science ®Google Scholar
• D. Y. Tzou, J. K. Chen, and J. E. Beraun, “Recent development of ultrafast thermoelasticity,” J. Therm. Stress., vol. 28, no. 6-7, pp. 563–594, 2005. DOI: 10.1080/01495730590929359.
   Web of Science ®Google Scholar
• T.-W. Tsai and Y.-M. Lee, “Analysis of microscale heat transfer and ultrafast thermoelasticity in a multi-layered metal film with nonlinear thermal boundary resistance,” Int. J. Heat Mass Transf., vol. 62, pp. 87–98, 2013. DOI: 10.1016/j.ijheatmasstransfer.2013.02.048.
   Web of Science ®Google Scholar
• D. Yu Tzou, Macro- to Microscale Heat Transfer: The Lagging Behavior. Series in chemical and mechanical engineering, 2nd ed. Chichester, UK: Wiley, 2015. DOI: 10.1002/9781118818275.
   Google Scholar
• A. Entezari, M. Filippi, E. Carrera, and M. A. Kouchakzadeh, “3D dynamic coupled thermoelastic solution for constant thickness disks using refined 1D finite element models,” Appl. Math. Model., vol. 60, pp. 273–285, 2018. DOI: 10.1016/j.apm.2018.03.015.
   Web of Science ®Google Scholar
• A. N. Sinha and S. B. Sinha, “Reflection of thermoelastic waves at a solid half-space with thermal relaxation,” J. Phys. Earth, vol. 22, no. 2, pp. 237–244, 1974. DOI: 10.4294/jpe1952.22.237.
   Google Scholar
• J. N. Sharma and V. Pathania, “Generalized thermoelastic wave propagation in circumferential direction of transversely isotropic cylindrical curved plates,” J. Sound Vib., vol. 281, no. 3-5, pp. 1117–1131, 2005. DOI: 10.1016/j.jsv.2004.02.010.
   Web of Science ®Google Scholar
• Y. Jiangong, W. Bin, and H. Cunfu, “Circumferential thermoelastic waves in orthotropic cylindrical curved plates without energy dissipation,” Ultrasonics, vol. 50, no. 3, pp. 416–423, 2010. DOI: 10.1016/j.ultras.2009.09.031.
   PubMed Web of Science ®Google Scholar
• I. Dobovšek, “Structure and intrinsic properties of dispersion relation in hyperbolic thermoelasticity,” J. Therm. Stress., vol. 39, no. 10, pp. 1200–1209, 2016. DOI: 10.1080/01495739.2016.1215725.
   Web of Science ®Google Scholar
• T. E. Tay, “Finite element analysis of thermoelastic coupling in composites,” Comput. Struct., vol. 43, no. 1, pp. 107–112, 1992. DOI: 10.1016/0045-7949(92)90084-D.
   Web of Science ®Google Scholar
• D. Palumbo and U. Galietti, “Data correction for thermoelastic stress analysis on titanium components,” Exp. Mech., vol. 56, no. 3, pp. 451–462, Mar. 2016. DOI: 10.1007/s11340-015-0115-0.
   Web of Science ®Google Scholar
• R. J. Greene, E. A. Patterson, and R. E. Rowlands, “Thermoelastic stress analysis,” in Springer Handbook of Experimental Solid Mechanics, W. N. Sharpe, ed. Boston, MA: Springer, 2008; pp. 743–768.
   Google Scholar
• P. Stanley, “Beginnings and early development of thermoelastic stress analysis,” Strain, vol. 44, no. 4, pp. 285–297, 2008. DOI: 10.1111/j.1475-1305.2008.00512.x.
   Web of Science ®Google Scholar
• M. H. Belgen, “Infrared radiometric stress instrumentation application range study,” NASA Contractor Report, NASA CR-1067, NASA, Washington D.C., 1968.
   Google Scholar
• A. K. Wong, R. Jones, and J. G. Sparrow, “Thermoelastic constant or thermoelastic parameter?” J. Phys. Chem. Solids, vol. 48, no. 8, pp. 749–753, 1987. DOI: 10.1016/0022-3697(87)90071-0.
   Web of Science ®Google Scholar
• G. Pitarresi and E. A. Patterson, “A review of the general theory of thermoelastic stress analysis,” J. Strain Anal. Eng. Des., vol. 38, no. 5, pp. 405–417, 2003. DOI: 10.1243/03093240360713469.
   Web of Science ®Google Scholar
• R. B. Hetnarski and M. Reza Eslami, Thermal Stresses – Advanced Theory and Applications. Volume 158 of solid mechanics and its applications. Dordrecht, Netherlands: Springer, 2009.
   Google Scholar
• M. A. Ezzat, M. I. Othman, and A. S. El-Karamany, “The dependence of the modulus of elasticity on the reference temperature in generalized thermoelasticity,” J. Therm. Stress., vol. 24, no. 12, pp. 1159–1176, 2001. DOI: 10.1080/014957301753251737.
   Web of Science ®Google Scholar
• M. I. A. Othman, “Lord–Shulman theory under the dependence of the modulus of elasticity on the reference temperature in two-dimensional generalized thermoelasticity,” J. Therm. Stress., vol. 25, no. 11, pp. 1027–1045, 2002. DOI: 10.1080/01495730290074621.
   Web of Science ®Google Scholar
• H. M. Youssef and I. A. Abbas, “Thermal shock problem of generalized thermoelasticity for an infinitely long annular cylinder with variable thermal conductivity,” Comput. Methods Sci. Technol., vol. 13, no. 2, pp. 95–100, 2007. DOI: 10.12921/cmst.2007.13.02.95-100.
   Google Scholar
• A. M. Zenkour and I. A. Abbas, “A generalized thermoelasticity problem of an annular cylinder with temperature-dependent density and material properties,” Int. J. Mech. Sci., vol. 84, no. Supplement C, pp. 54–60, 2014. DOI: 10.1016/j.ijmecsci.2014.03.016.
   Google Scholar
• A. Kumar and S. Mukhopadhyay, “Investigation on the effects of temperature dependency of material parameters on a thermoelastic loading problem,” Z. Angew. Math. Physik, vol. 68, no. 4, pp. 98, Aug. 2017. DOI: 10.1007/s00033-017-0843-3.
   Web of Science ®Google Scholar
• O. W. Dillon, “A nonlinear thermoelasticity theory,” J. Mech. Phys. Solids, vol. 10, no. 2, pp. 123–131, 1962. DOI: 10.1016/0022-5096(62)90015-7.
   Web of Science ®Google Scholar
• H. W. Lord and Y. Shulman, “A generalized dynamical theory of thermoelasticity,” J. Mech. Phys. Solids, vol. 15, no. 5, pp. 299–309, 1967. DOI: 10.1016/0022-5096(67)90024-5.
   Web of Science ®Google Scholar
• H. G. Wang, “The expression of free energy for thermoelastic material and its relation to the variable material coefficients,” Appl. Math. Mech., vol. 9, no. 12, pp. 1139–1144, 1988. DOI: 10.1007/BF02014468.
   Google Scholar
• E. D. Marquardt, J. P. Le, and R. Radebaugh, “Cryogenic material properties database,” in Cryocoolers 11, R. G. Ross, ed. Boston, MA: Springer, 2002. DOI: 10.1007/0-306-47112-4_84.
   Google Scholar
• A. D. Kovalenko, Osnovy Termouprugosti. Kiev: Naukova Dumka, 1970.
   Google Scholar
• A. D. Kovalenko, “The current theory of thermoelasticity,” Int. Appl. Mech., vol. 6, no. 4, pp. 355–360, 1970. DOI: 10.1007/BF00889364.
   Google Scholar
• D. E. Carlson, “Linear thermoelasticity,” in Linear Theories of Elasticity and Thermoelasticity, C. Truesdell, ed. Berlin: Springer, 1973.
   Google Scholar
• D. Boussaa, “On thermodynamic potentials in thermoelasticity under small strain and finite thermal perturbation assumptions,” Int. J. Solids Struct., vol. 51, no. 1, pp. 26–34, 1, 2014. DOI: 10.1016/j.ijsolstr.2013.09.009.
   Web of Science ®Google Scholar
• D. Boussaa, “Effects of superimposed eigenstrains on the overall thermoelastic moduli of composites,” Mech. Mater., vol. 104, pp. 26–37, 2017. DOI: 10.1016/j.mechmat.2016.10.001.
   Web of Science ®Google Scholar
• J. Lubliner, Plasticity Theory. New York: Macmillan Publishing Company and London: Collier Macmillan Publishers, 1990.
   Google Scholar
• D. S. Chandrasekharaiah, “Thermoelasticity with second sound: a review,” Appl. Mech. Rev., vol. 39, no. 3, pp. 355–376, 03, 1986. DOI: 10.1115/1.3143705.
   Google Scholar
• D. S. Chandrasekharaiah, “Hyperbolic thermoelasticity: a review of recent literature,” Appl. Mech. Rev., vol. 51, no. 12, pp. 705–729, 1998. DOI: 10.1115/1.3098984.
   Google Scholar
• R. Fu, “Thermo-mechanical coupling for ablation,” PhD thesis, University of Kentucky, Lexington, Kentucky, 2018.
   Google Scholar
• A. F. Robinson, J. M. Dulieu-Barton, S. Quinn, and R. L. Burguete, “A review of residual stress analysis using thermoelastic techniques,” J. Phys. Conf. Ser., vol. 181, no. 1, pp. 012029, 2009. DOI: 10.1088/1742-6596/181/1/012029.
   Google Scholar
• A. F. Robinson, J. M. Dulieu-Barton, S. Quinn, and R. L. Burguete, “Paint coating characterization for thermoelastic stress analysis of metallic materials,” Meas. Sci. Technol., vol. 21, no. 8, pp. 085502, 2010. DOI: 10.1088/0957-0233/21/8/085502.
   Web of Science ®Google Scholar
• A. Garinei, M. Becchetti, E. Pucci, and G. Rossi, “Constant stress field measurements through thermoelasticity,” J. Therm. Stress., vol. 36, no. 7, pp. 672–683, 2013. DOI: 10.1080/01495739.2013.770700.
   Web of Science ®Google Scholar
• G. Howell, M. Achintha, J. M. Dulieu-Barton, and A. F. Robinson, “A stress-free model for residual stress assessment using thermoelastic stress analysis,” in International Conference on Experimental Mechanics (icEM2014), vol. 9302, C. Quan, K. Qian, A. Asundi, and F. Siong Chau, Eds. Bellingham, WA: SPIE, 2015.
   Google Scholar
• G. Howell, “Identification of plastic strain using thermoelastic stress analysis.” PhD thesis, University of Southampton, Southampton, UK, 2017.
   Google Scholar
• A. S. Machin, J. G. Sparrow, and M. G. Stimson, “Mean stress dependence of the thermoelastic constant,” Strain, vol. 23, no. 1, pp. 27–30, 1987. DOI: 10.1111/j.1475-1305.1987.tb01934.x.
   Google Scholar